Geodesic
Path Integrals on Euclidean Space Forms
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed. In the $\mathbb{R}^n$ case the obtained results coincide with the known expressions.
Keywords: path integrals; holomorphic quantization; space forms; reproducing kernel Hilbert spaces. 
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     author = {Guillermo Capobianco and Walter Reartes},
     title = {Path {Integrals} on {Euclidean} {Space} {Forms}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a70/}
}
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Guillermo Capobianco; Walter Reartes. Path Integrals on Euclidean Space Forms. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a70/

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